Seems like it would be a little difficult to pull of since the color palette is so limited. However, here is a reference that shows a bit of texture in the wood using brown. Hope this helps

The background is dark, yet the treetops and ground look too bright. And maybe would be interesting to choose one or some light sources as your next move.

No one suggested adding more colours xP There's more to making things darker than just shifting the colours over one  - the distribution of those colours has just as much impact. In addition, you could suggest a different direction of the light depending on what you're going for.

I think the four colours you chose could use some work. Your two lightest colours are quite similar, so they're not very effective.
The values of your four greens are approximately, from darkest to lightest, 38%, 67%, 85%, 95% - hardly even coverage of the value scale. To demonstrate this, the jumps in value are 29%, 18%, 10% - if your palette covered the values evenly, these jumps would be pretty similar.
It's not inherently bad to have uneven coverage, but I think in this case, where you have just four colours and they have to be able to depict just about anything, it would benefit you to have a more even spread.

Here's an edit that adjusts the middle two colours so that they're evenly spaced between your darkest and lightest:

I think this makes your existing pixel work read much better, particularly the wood texture and leaves.

Speaking of the wood texture, here's an example you might find useful:

The colours here are weird just because of palette restrictions, don't mind them. The texture goes all through the wood, but the colours are sufficiently low-contrast that it doesn't stand out too much. The texture itself is mostly vaguely concentric ovals. Lots of arcs rather than disconnected lines.